Joined: Aug 2010
Posts: 12,717
Likes: 2,104
From: Madison, WI
Bikes: 1961 Ideor, 1966 Perfekt 3 Speed AB Hub, 1994 Bridgestone MB-6, 2006 Airnimal Joey, 2009 Thorn Sherpa, 2013 Thorn Nomad MkII, 2015 VO Pass Hunter, 2017 Lynskey Backroad, 2017 Raleigh Gran Prix, 1980s Bianchi Mixte on a trainer. Others are now gone.
I suspect you do not want to be removing the batteries to charge them. Thus, I suspect you want Li Ion batteries, but you did not specify.
Thus, I do not think you would be interested in what I use for taillights. I use AAA powered Planet Bike Superflash or Superflash 65 lights. And I use NiMH rechargeable AAA batteries. When touring I bring a USB powered NiMH AAA and AA charger. That meets your stated criteria, but I am removing the batteries from the light to charge them once a week.
Headlights, there are AAA powered lights too, thus you can run them on NiMH AAA batteries. But I have not bought one for over a decade, so I am not going to suggest one that probably is no longer made..
For home use I use an Accupower IQ328 AA/AAA charger, but I use a lot of AA and AAA batteries, so I invested in a top notch charger and this one is not USB powered.